Dr. Ben Heuer

Institut für Mathematik
Johann Wolfgang Goethe-Universität
Robert-Mayer-Str. 6-8
60325 Frankfurt am Main, Germany

Office: 211
E-Mail: heuer"at"math.uni-frankfurt.de
Group: Algebra and Geometry

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Research

I am a Postdoc at the University of Frankfurt. I am interested in arithmetic and algebraic geometry. My current projects are related to:

• p-adic non-abelian Hodge theory
• perfectoid geometry
• p-adic automorphic forms

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Publications and Preprints

• \(p\)-adic non-abelian Hodge theory for curves via moduli stacks
  with Daxin Xu
  Preprint 2024 (submitted)[ arXiv ]
• The relative Hodge-Tate spectral sequence for rigid analytic spaces
  Preprint 2024 [ arXiv ]
• The Primitive Comparison Theorem in characteristic \(p\)
  Preprint 2024 [ arXiv ]
• The small \(p\)-adic Simpson correspondence in terms of moduli spaces
  with Johannes Anschütz and Arthur-César Le Bras
  Preprint 2023 (submitted) [ arXiv ]
• \(p\)-adic Simpson correspondences for principal bundles in abelian settings
  with Annette Werner and Mingjia Zhang
  Preprint 2023 (submitted) [ arXiv ]
• A \(p\)-adic Simpson correspondence for smooth proper rigid varieties
  Preprint 2023 (submitted) [ arXiv ]
• Hodge-Tate stacks and non-abelian \(p\)-adic Hodge theory of v-perfect complexes
  with Johannes Anschütz and Arthur-César Le Bras
  Preprint 2023 (submitted) [ arXiv ]
• v-vector bundles on \(p\)-adic fields and Sen theory via the Hodge-Tate stack
  with Johannes Anschütz and Arthur-César Le Bras
  Preprint 2022 (submitted) [ arXiv ]
• Moduli spaces in \(p\)-adic non-abelian Hodge theory
  Preprint 2022 (submitted) [ arXiv ]
• \(G\)-torsors on perfectoid spaces
  Preprint 2022 [ arXiv ]
• Pro-étale uniformisation of abelian varieties
  Preprint 2021 [ arXiv ]
• Line bundles on perfectoid covers: case of good reduction
  Preprint 2021 [ arXiv ]
• Diamantine Picard functors of rigid spaces
  Preprint 2021 (submitted) [ arXiv ]
• A geometric \(p\)-adic Simpson correspondence in rank one
  Accepted at Compositio Math. [ arXiv ]
• The $p$-adic Corlette-Simpson correspondence for abeloids
  with Lucas Mann, Annette Werner
  Math. Ann. 2022. [ arXiv ]
• Line bundles on rigid spaces in the v-topology
  Forum Math. Sigma 2022. [ arXiv ]
• Overconvergent Hilbert modular forms via perfectoid modular varieties
  with Christopher Birkbeck, Chris Williams
  Ann. Inst. Fourier, 2022. [ arXiv ]
• Perfectoid covers of abelian varieties
  with Clifford Blakestad, Damián Gvirtz, Daria Shchedrina, Koji Shimizu, Peter Wear, Zijian Yao
  Math. Res. Lett. 29.3: 631-662 (2022). [ arXiv ]
• Cusps and $q$-expansion principles for modular curves at infinite level
  Doc. Math. 27, 2385-2439 (2022) [ arXiv ]
• Perfectoid geometry of $p$-adic modular forms
  PhD thesis 2019, London School of Geometry and Number Theory
• Rigid $\tau$-crystals
  Journal de Théorie des Nombres de Bordeaux 29(3):1059-1082, 2017.
  
• All solutions to the immobilizer problem
  with John Conway
  Math. Intelligencer 36(4):78-86, 2014.
  
• Proof-reading guidance in cell tracking by sampling tracking-by-assignment models
  with Martin Schiegg, Carsten Haubold, Steffen Wolf, Ulrich Koethe, Fred A Hamprecht
  In Biomedical Imaging (ISBI), 2015 IEEE 12th International Symposium
  

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Teaching and Seminars

• In the summer term 2023, with Annette Werner and Katharina Hübner, we organised a research seminar (GAUS seminar) on Non-archimedean Geometry. The seminar page can be found here.

• Im Sommersemester 2023 war ich Assistent für die Lineare Algebra 2 bei Prof. Werner. Die Website der Vorlesung ist hier.

• Im Wintersemester 22/23 habe ich ein L3-Seminar an der Goethe Universität Frankfurt zum Thema Geschichte der Mathematik veranstaltet. Die Liste der Vorträge finden Sie hier.

• Im Wintersemester 22/23 habe ich mit Prof. Annette Werner ein Proseminar/L3-Seminar an der Goethe Universität Frankfurt zum Thema Beweismethoden veranstaltet. hier.

• In the summer term 22, I taught a lecture course on Rigid Analytic Geometry. The course gave an introduction to non-archimedean geometry by discussing in detail Tate's rigid analytic spaces. Thanks very much to Matthew Stevens for TeXing lecture notes and for letting me share them with you here! [They're "unofficial" notes as I can't guarantee that they represent exactly what was said in the lecture, so for exam preparation use at your own risk].

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Events

• In March 2023, I gave a course on perfectoid spaces at the Heidelberg Spring School on non-archimedean geometry and eigenvarieties, from 6-17th March 2023.
• With Johannes Anschütz and Arthur-César Le Bras, we organised a workshop on the recent work of Lue Pan, from 20-25th November 2022 at Maison Du Kleebach. Here is the program.
• I co-organised the conference "Graduate Opportunities for Women (GROW)" in Bonn. Details can be found here.
• With Mingjia Zhang I organised a Kleine AG on 12 March 2022. Details and notes can be found here.

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Last update: April 2024, Ben Heuer